Nonparametric prediction intervals for future record intervals based on order statistics

In this article, outer and inner prediction intervals for future record intervals as well as record spacings are derived based on observed order statistics from the same parent distribution. These intervals are exact and are distribution-free in that they do not depend on the sampling distribution. Three different cases are considered and in each case an exact explicit expression is obtained for the prediction coefficient. Finally, we compare the obtained results with similar intervals based on records, and also present a numerical example in order to illustrate the derived results.     

Computational aspects of statistical intervals based on two Type-II censored samples

In this paper, we propose an efficient branch and bound procedure to compute exact nonparametric statistical intervals based on two Type-II right censored data sets. The procedure is based on some recurrence relations for the distribution and density functions of progressively Type-II censored order statistics which can be applied to compute the coverage probabilities. We illustrate the method for both confidence and prediction intervals of a given level.     

Two sample Bayesian prediction intervals for order statistics based on the inverse exponential-type distributions using right censored sample

In this paper, two sample Bayesian prediction intervals for order statistics (OS) are obtained. This prediction is based on a certain class of the inverse exponential-type distributions using a right censored sample. A general class of prior density functions is used and the predictive cumulative function is obtained in the two samples case. The class of the inverse exponential-type distributions includes several important distributions such the inverse Weibull distribution, the inverse Burr distribution, the loglogistic distribution, the inverse Pareto distribution and the inverse paralogistic distribution. Special cases of the inverse Weibull model such as the inverse exponential model and the inverse Rayleigh model are considered.     

Initial conditions estimation for improving forecast accuracy in exponential smoothing

In this paper we analyze the importance of initial conditions in exponential smoothing models on forecast errors and prediction intervals. We work with certain exponential smoothing models, namely Holt’s additive linear and Gardner’s damped trend. We study some probability properties of those models, showing the influence of the initial conditions on the forecast, which highlights the importance of obtaining accurate estimates of initial conditions. Using the linear heteroscedastic modeling approach, we show how to obtain the joint estimation of initial conditions and smoothing parameters through maximum likelihood via box-constrained nonlinear optimization. Point-wise forecasts of future values and prediction intervals are computed under normality assumptions on the stochastic component. We also propose an alternative formulation of prediction intervals in order to obtain an empirical coverage closer to their nominal values; that formulation adds an additional term to the standard formulas for the estimation of the error variance. We illustrate the proposed approach by using the yearly data time-series from the M3-Competition.     

Bayesian prediction for the two-parameter exponential distribution based on type II doubly censoring

The two-parameter exponential distribution is proposed to be an underlying model, and prediction bounds for future observations are obtained by using Bayesian approach. Prediction intervals are derived for unobserved lifetimes in one-sample prediction and two-sample prediction based on type II doubly censored samples. A numerical example is given to illustrate the procedures, prediction intervals are investigated via Monte Carlo method, and the accuracy of prediction intervals is presented. Supported by the National Natural Science Foundation of China (79970022) and Aviation Fund (02J53079).     

Dynamic Data-Driven Genetic Algorithm for forest fire spread prediction

This work represents the first step towards a Dynamic Data-Driven Application System (DDDAS) for wildland fire prediction. Our main efforts are focused on taking advantage of the computing power provided by High Performance Computing systems and to propose computational data-driven steering strategies to overcome input data uncertainty. In doing so, prediction quality can be enhanced significantly. On the other hand, these proposals reduce the execution time of the overall prediction process in order to be of use during real-time crisis. In particular, this work describes a Dynamic Data-Driven Genetic Algorithm (DDDGA) used as steering strategy to automatically adjust highly dynamic input data values of forest fire simulators taking into account the underlying propagation model and real fire behaviour.     

Optimal plan for Wiener constant-stress accelerated degradation model

This paper explores inferential procedures for the Wiener constant-stress accelerated degradation model under degradation mechanism invariance. The exact confidence intervals are obtained for the parameters of the proposed accelerated degradation model. The generalized confidence intervals are also proposed for the reliability function and pth quantile of the lifetime at the normal operating stress level. In addition, the prediction intervals are developed for the degradation characteristic, lifetime and remaining useful life of the product at the normal operating stress level. The performance of the proposed generalized confidence intervals and the prediction intervals is assessed by the Monte Carlo simulation. Furthermore, a new optimum criterion is proposed based on minimizing the mean of the upper prediction limit for the degradation characteristic at the design stress level. The exact optimum plan is also derived for the Wiener accelerated degradation model according to the proposed optimal criterion. The proposed interval procedures and optimum plan are the free of the equal testing interval assumption. Finally, two examples are provided to illustrate the proposed interval procedures and exact optimum plan. Specifically, based on the degradation data of LEDs, some interval estimates of quantities related to reliability indicators are obtained. For the degradation data of carbon-film resistors, the optimal allocation of test units is derived in terms of the proposed optimal criterion.     

Nonparametric prediction intervals for progressive Type-II censored order statistics based on k-records

In this paper, we consider the prediction problem in two-sample case and study the non-parametric predicting future progressively Type-II censored order statistics based on observed $k$ -records from the same distribution. Also, prediction intervals for progressively Type-II censored spacings are obtained based on $k$ -record spacings. It is shown that the coverage probabilities of these intervals are exact and do not depend on the underlying distribution. Moreover, optimal prediction intervals are derived for each case. Finally, for illustrating the proposed procedure, we consider a real data set and numerical computations are given. The results of Ahmadi and Balakrishnan (Statistics 44:417–430, 2010) can be achieved as special cases of our results.     

Confidence prediction of the mean values of multiple observations

The confidence prediction of the mean value ofmultiple responses in a linear multivariate normal regression model is considered. In order to solve it, confidence intervals of the mean value of multiple responses and its predicted value are obtained. They are numerically modeled and analyzed in comparison with known analogues for regression and individual response.     

Semiqualitative modelling of bioprocesses

This paper deals with semiqualitative modelling of bioprocesses with a view to their supervision. An analysis of several approaches for modelling shows the difficulties involved in taking into account in a same framework, quantitative and qualitative knowledge, generally available about a process that we want to control. We propose an original approach, placed in the context of semiqualitative modelling, that is supported by a knowledge model the variables and parameters of which are defined by intervals. For these semiqualitative models, we study their properties in simulation and prediction, and more precisely, their fitting based on experimental data. We show that pertinent predictions in a short time can be obtained, making of these semiqualitative models interesting tools for the development of systems for bioprocess supervision     

Prediction interval for disease mapping using hierarchical likelihood

In disease mapping, the Bayesian approach is widely used for forming the prediction interval of relative risks. In this paper we propose a hierarchical-likelihood interval for disease mapping, which accounts for the inflation of standard error estimates caused by uncertainty in the estimation of the fixed parameters. Comparison is made with the Bayesian prediction intervals derived from penalized quasi-likelihood and fully Bayesian methods. Through simulation studies, we show that prediction intervals for random effects using hierarchical likelihood maintains the required level.     

Bayesian forecasting with the Holt–Winters model

Exponential smoothing methods are widely used as forecasting techniques in inventory systems and business planning, where reliable prediction intervals are also required for a large number of series. This paper describes a Bayesian forecasting approach based on the Holt–Winters model, which allows obtaining accurate prediction intervals. We show how to build them incorporating the uncertainty due to the smoothing unknowns using a linear heteroscedastic model. That linear formulation simplifies obtaining the posterior distribution on the unknowns; a random sample from such posterior, which is not analytical, is provided using an acceptance sampling procedure and a Monte Carlo approach gives the predictive distributions. On the basis of this scheme, point-wise forecasts and prediction intervals are obtained. The accuracy of the proposed Bayesian forecasting approach for building prediction intervals is tested using the 3003 time series from the M3-competition.     

The Karush–Kuhn–Tucker optimality conditions in an optimization problem with interval-valued objective function

The KKT conditions in an optimization problem with interval-valued objective function are derived in this paper. Two solution concepts of this optimization problem are proposed by considering two partial orderings on the set of all closed intervals. In order to consider the differentiation of an interval-valued function, we invoke the Hausdorff metric to define the distance between two closed intervals and the Hukuhara difference to define the difference of two closed intervals. Under these settings, we derive the KKT optimality conditions.     

Do forecasts expressed as prediction intervals improve production planning decisions?

A number of studies have shown that providing point forecasts to decision makers can lead to improved production planning decisions. However, point forecasts do not convey information about the level of uncertainty that is associated with forecasts. In theory, the provision of prediction intervals, in addition to point forecasts, should therefore lead to further enhancements in decision quality. To test whether this is the case in practice, participants in an experiment were asked to decide on the production levels that were needed to meet the following week’s demand for a series of products. Either underproduction cost twice as much per unit as overproduction or vice versa. The participants were supplied with either a point forecast, a 50% prediction interval, or a 95% prediction interval for the following week’s demand. The prediction intervals did not improve the quality of the decisions and also reduced the propensity of the decision makers to respond appropriately to the asymmetry in the loss function. A simple heuristic is suggested to allow people to make more effective use of prediction intervals. It is found that applying this heuristic to 85% prediction intervals would lead to nearly optimal decisions.     

Weibull过程将来第k次失效时间的Bayes预测区间

具Weibull强度函数的非齐次Poisson过程经常被用来分析可修系统的失效模式.基于极大似然估计,Engelhardt ＆ Bain(1978)导出了Weibull过程将来第k次失效时间的经典预测区间.在本文中,我们用无信息联合验前分布,根据Weibull过程的前n次失效时间,给出了建立将来第k次失效时间的Bayes预测区间的方法,并说明了如何应用这些方法。     

The Karush–Kuhn–Tucker optimality conditions in multiobjective programming problems with interval-valued objective functions

The KKT conditions in multiobjective programming problems with interval-valued objective functions are derived in this paper. Many concepts of Pareto optimal solutions are proposed by considering two orderings on the class of all closed intervals. In order to consider the differentiation of an interval-valued function, we invoke the Hausdorff metric to define the distance between two closed intervals and the Hukuhara difference to define the difference of two closed intervals. Under these settings, we are able to consider the continuity and differentiability of an interval-valued function. The KKT optimality conditions can then be naturally elicited.     

Prediction and calibration in generalized linear models

This paper concerns prediction and calibration in generalized linear models. A new predictive procedure, giving improved prediction intervals, is briefly reviewed and further theoretical results, useful for calculations, are presented. Indeed, the calibration problem is faced within the classical approach and a suitable solution is obtained by inverting the associated improved prediction procedure. This calibration technique gives accurate confidence regions and it constitutes a substantial improvement over both the estimative solution and the naive solution, which involves, even for non-linear and non-normal models, the results available for the linear Gaussian case. Finally, some useful explicit formulae for the construction of prediction and calibration intervals are presented, with regard to generalized linear models with alternative error terms and link functions. This research was partially supported by a grant from Ministero dell’Instruzione, dell’Università e della Ricerca, Italy.     

基于SSA的金融时间序列自适应分解预测

提出了分解预测的思想,通过SSA将序列分解成低频与高频两部分,分别采用最小均方(LMS)自适应自回归移动平均(ARIMA)与LMS自适应自回归(AR)模型进行预测,然后将两者叠加便可得原始序列预测值.同时,为了更好地捕捉序列局部突变,缩减预测延迟,提高预测精度,对EaLMS算法(基于误差调整的LMS算法)参数进行修正并...     

Large sample prediction intervals for future geometric mean a comparative study

This paper provides simulation comparisons among the performance of 11 possible prediction intervals for the geometric.mean of a Pareto distribution with parameters (αB, ). Six different procedures were used to obtain these intervals , namely; true inter -val , pivotal interval , maximum likelihood estimation interval, centrallimit teorem interval, variance stabilizing interval and a mixture of the above intervals . Some of these intervals are valid if the observed sample size m,are large , others are valid if both, n and the future sample size m, are large. Some of these intervals require a knowledge of α or B, while others do not. The simulation validation and efficiency study shows that intervals depending on the MLE's are the best. The second best intervalsare those obtained through pivotal methods or variance stabilization transformation. The third group of intervals is that which depends on the central limit theorem when λ is known. There are two intervals which proved to be unacceptable under any criterion.     

神经网络优化组合预测模型在油气产量预测中的应用

采用组合预测方法对油气产量预测进行研究,首先选取油藏工程领域多种油气产量预测模型建立组合预测模型库,基于权系数的时效性,利用三层前馈BP神经网络建立油气产量变权组合预测模型,并进行实例分析,结果表明该方法能提高预测精度,增强预测模型的实用性.